CN109765950B - Control method for first-order pure time delay furnace temperature system - Google Patents

Abstract

The invention discloses a first-order pure time delay furnace temperature system control method, which comprises the following steps: s1: setting and deducing parameters of a first-order pure time delay model; s2: designing a system structure; s3: designing a controller; s4: and comparing the simulation results to obtain a conclusion. The controller structure designed by the invention has the characteristics of better tracking input signals and effectively inhibiting disturbance signals, and can be used for controlling a first-order pure time delay furnace temperature system.

Description

Control method for first-order pure time delay furnace temperature system

Technical Field

The invention relates to a control method of a first-order pure time delay furnace temperature system, and belongs to the technical field of industrial time delay control systems.

Background

Generally, in an industrial production process control system, a time delay phenomenon generally exists, and due to the existence of the time delay, a controlled quantity cannot reflect disturbance borne by the system in time, so that a system dynamic error is increased, a stability margin is reduced, and even system oscillation is caused. Therefore, the control method of the delay system is always a hot problem to be researched in control theory and control engineering, and many scholars propose various design methods of controllers for the delay system. At present, the research on the time delay system is mainly based on the traditional Smith estimation controller, and the following research is carried out: one is to carry out structural optimization on the Smith estimation controller; one is to combine the Smith estimation controller with PID parameter setting method; and the other type of the method mainly combines a Smith prediction controller with advanced control methods such as fuzzy control and neural network.

Disclosure of Invention

The invention provides a control method of a first-order pure time delay furnace temperature system aiming at the defects in the prior art, solves the technical problems in the background art, and meets the actual use requirements.

In order to solve the problems, the technical scheme adopted by the invention is as follows:

a control method for a first-order pure time delay furnace temperature system comprises the following steps:

s1: parameter setting and derivation of first-order pure time delay model

In the field of industrial control, especially in the processing of metal materials and the control of fluids, the temperature of a heating furnace directly affects the quality of processed materials and the utilization efficiency of energy, the heating furnace is a temperature with pure time delay and time constant, and the heating furnace is taken as a control object, and comprises the following components:

u-voltage at two ends of the electric heating wire;

T₁-post-heating furnace temperature;

Q_i-unit ofHeat generated by the heating wire over time;

the mass of the electric heating wire is M, the specific heat is C, the heat transfer area is A, and the temperature in the furnace before heating is T₀The furnace temperature after heating is T₁According to the thermodynamic principle, there are

Q_iProportional to the square of u, i.e. Q_iIs in a nonlinear relationship with u, and is at equilibrium point (Q)₀,u₀) Carrying out linearization to obtain K_u＝ΔQ_iAnd/Δ u, the incremental equation of the heating furnace is as follows:

in the formula: Δ T ═ T₁-T₀，T＝MC/HA，K＝K_u/HA

The transfer function is obtained from equation (2)

However, the actual heating furnace system has a certain thermal inertia during response, so that the system has a time delay τ, and therefore, the furnace temperature of the heating furnace can be represented by a first-order pure time delay model as follows:

s2: design of system architecture

It includes: x_r(s) is the system input quantity, X_c(s) system output, G(s) controlled object model, G_f(s) is a feedback channel controller, D(s) is a front channel controller, X_d1(s) is the system input disturbance and X_d2(s) is the system output disturbance;

then there are: system at input quantity X_rThe closed loop transfer function under the action of(s) is:

the system is inputting disturbance X_d1The closed loop transfer function under the action of(s) is:

the system is outputting disturbance X_d2The closed loop transfer function under the action of(s) is:

s3: designing a controller:

the method comprises the following steps: forward channel controller D(s) design and feedback channel controller G_f(s) design

Where β is an adjustable parameter, and when β < 1, the Taylor series expansion according to the e-exponential function

The forward channel controller d(s) can be written as:

leading: considering the system configuration described in S2, let

k_p＝α(τ+β)0≤α＜1 (11)

The following steps are performed:

to ensure stability of the closed loop system, the gain k_dIt can be set as follows:

here, the first and second liquid crystal display panels are,

representing the phase margin of the system, and 0 ≦ α < 1, β being an adjustable parameter, it may be shown that when selecting α ≦ 0.4,

the stability and robustness of the time-closed loop can be satisfied;

thus, the gain k_dCan be simplified as follows:

response of the system when a step input is applied to the system:

response under step input perturbation:

response under step output perturbation:

the system has good step tracking and step disturbance effects;

s4: and comparing the simulation results to obtain a conclusion.

Compared with the prior art, the invention has the following implementation effects:

the controller structure designed by the invention has the characteristics of better tracking input signals and effectively inhibiting disturbance signals, and can be used for controlling a first-order pure time delay furnace temperature system.

Drawings

FIG. 1 is a schematic view of a furnace according to an embodiment of the present invention;

FIG. 2 is a schematic structural diagram of a control system according to an embodiment of the present invention;

FIG. 3 is a schematic diagram of simulation result coordinates of the control method of the present invention and the conventional Smith control method;

FIG. 4 is a schematic diagram of time response coordinates of the control system of the present invention in the presence of a disturbance.

Detailed Description

The present invention will be described with reference to specific examples.

First, problem description (first-order pure time delay model parameter setting and derivation)

In the field of industrial control, especially in the processing of metal materials and the control of fluids, the furnace temperature of a heating furnace directly affects the quality of processed materials and the utilization efficiency of energy, the heating furnace is a temperature with pure time delay and time constant, the heating furnace is a control object, and the structural schematic diagram is shown in fig. 1:

in the figure, u-voltage at two ends of the electric heating wire;

T₁-post-heating furnace temperature;

Q_i-the heat generated by the heating wire per unit time;

if the mass of the electric heating wire is M, the specific heat is C, the heat transfer area is A, and the temperature in the furnace before heating is T₀The furnace temperature after heating is T₁According to the thermodynamic principle, there are

Q_iProportional to the square of u, i.e. Q_iIs in a nonlinear relationship with u, and is at equilibrium point (Q)₀,u₀) Carrying out linearization to obtain K_u＝ΔQ_iΔ u, then the incremental equation of the furnace is

Wherein Δ T ═ T₁-T₀，T＝MC/HA，K＝K_u/HA

The transfer function is obtained from equation (2)

However, the actual heating furnace system has a certain thermal inertia during response, so that the system has a time delay τ, and therefore, the furnace temperature of the heating furnace can be represented by a first-order pure time delay model as follows:

second, system structure design

The structure of a typical control system designed by the invention is shown in FIG. 2: wherein, X_r(s) is the system input quantity, X_c(s) system output, G(s) controlled object model, G_f(s) is a feedback channel controller, D(s) is a front channel controller, X_d1(s) is the system input disturbance, X_d2(s) is the system output disturbance;

then the system inputs the quantity X_rThe closed loop transfer function under the action of(s) is:

the system is inputting disturbance X_d1The closed loop transfer function under the action of(s) is:

the system is outputting disturbance X_d2The closed loop transfer function under the action of(s) is:

third, controller design

For the first-order pure time delay furnace temperature system, in the structure of FIG. 2, a forward channel controller D(s) and a feedback channel controller G_f(s) can be designed as:

where β is an adjustable parameter, and when β < 1, the Taylor series expansion according to the e-exponential function

The forward channel controller d(s) can be written as:

leading: consider the system architecture as shown in FIG. 2, such that

k_p＝α(τ+β)0≤α＜1 (11)

The following steps are performed:

to ensure stability of the closed loop system, the gain k_dIt can be set as follows:

here, the first and second liquid crystal display panels are,

representing the phase margin of the system, and 0 ≦ α < 1, β being an adjustable parameter, it may be shown that when selecting α ≦ 0.4,

the stability and robustness of the time-closed loop can be satisfied.

Thus, the gain k_dCan be simplified as follows:

response of the system when a step input is applied to the system:

response under action of step input disturbance

Response under step output perturbation

This indicates that the system has good step tracking and step perturbation effects.

Fourth, simulation result

Considering the furnace temperature of a certain heating furnaceThe first order pure delay model is represented as:

assuming a given furnace temperature of 50 ℃, the simulation results are shown in fig. 3, using both the conventional Smith control method and the control method of the present invention. When the curve1 is beta-0.1, the simulation result of the control method is obtained; when the curve2 is beta is 0.4, the control method of the invention simulates the result; when curve3 is beta-1, the control method of the invention simulates the result.

As can be seen from fig. 3, in the method of the present invention, although the system response time is lengthened with the increase of the value of the adjustable parameter β, the time response characteristic is superior to that of the conventional Smith control method.

In addition, on the basis of the time response of fig. 3, when the system response time is 10 seconds and 25 seconds, respectively, the disturbance is added, and the system response result is shown in fig. 4; as can be seen from fig. 4, under the action of the disturbance signal, compared with the conventional Smith control method, the control method of the present invention still has a better time response characteristic, and can effectively suppress the interference effect.

The foregoing is a detailed description of the invention with reference to specific embodiments, and the practice of the invention is not to be construed as limited thereto. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (1)

1. A first-order pure time delay furnace temperature system control method is characterized in that: the control method comprises the following steps:

s1: parameter setting and derivation of first-order pure time delay model

In the field of industrial control, in the control of metal material processing fluid, the furnace temperature of a heating furnace directly influences the quality of processing material and the utilization efficiency of energy, and the heating furnace is taken as a control object and comprises the following steps:

u-voltage at two ends of the electric heating wire;

T₁-post-heating furnace temperature;

Q_i-the heat generated by the heating wire per unit time;

the mass of the electric heating wire is M, the specific heat is C, the heat transfer area is A, and the temperature in the furnace before heating is T₀The furnace temperature after heating is T₁According to the thermodynamic principle, there are

Wherein H represents a heat transfer coefficient

Q_iProportional to the square of u, i.e. Q_iIs in a nonlinear relationship with u, and is at equilibrium point (Q)₀,u₀) Carrying out linearization to obtain K_u＝ΔQ_iAnd/Δ u, the incremental equation of the heating furnace is as follows:

in the formula: Δ T ═ T₁-T₀，T＝MC/HA，K＝K_u/HA

The transfer function is obtained from equation (2)

However, the actual heating furnace system has a certain thermal inertia during response, so that the system has a time delay τ, and therefore, the furnace temperature of the heating furnace can be represented by a first-order pure time delay model as follows:

s2: design of system architecture

It includes: x_r(s) is the system input quantity, X_c(s) system output, G(s) controlled object model, G_f(s) is a back-feed-through controller, D(s) is a front-feed-through controller,X_d1(s) is the system input disturbance and X_d2(s) is the system output disturbance;

then there are: system at input quantity X_rThe closed loop transfer function under the action of(s) is:

the system is inputting disturbance X_d1The closed loop transfer function under the action of(s) is:

the system is outputting disturbance X_d2The closed loop transfer function under the action of(s) is:

s3: designing a controller:

the method comprises the following steps: feed-forward channel controller D(s) design and feed-back channel controller G_f(s) design

Where β is an adjustable parameter, and when β < 1, the Taylor series expansion according to the e-exponential function

Feed-forward channel controller D(s) can be written as:

leading: considering the system configuration described in S2, let

k_p＝α(τ+β)0≤α＜1 (11)

The following steps are performed:

to ensure stability of the closed loop system, the gain k_dIt can be set as follows:

here, the first and second liquid crystal display panels are,

representing the phase margin of the system, and 0 ≦ α < 1, β being an adjustable parameter, it may be shown that when selecting α ≦ 0.4,

the stability and robustness of the time-closed loop can be satisfied;

thus, the gain k_dCan be simplified as follows:

response of the system when a step input is applied to the system:

response under step input perturbation:

response under step output perturbation:

the system has good step tracking and step disturbance effects;

s4: and comparing the simulation results to obtain a conclusion.

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